# 1545. Find Kth Bit in Nth Binary String

Given two positive integers n and k, the binary string Sn is formed as follows:

S1 = "0" Si = Si-1 + "1" + reverse(invert(Si-1)) for i > 1 Where + denotes the concatenation operation, reverse(x) returns the reversed string x, and invert(x) inverts all the bits in x (0 changes to 1 and 1 changes to 0).

For example, the first 4 strings in the above sequence are:

S1 = "0" S2 = "011" S3 = "0111001" S4 = "011100110110001" Return the kth bit in Sn. It is guaranteed that k is valid for the given n.

Example 1:

Input: n = 3, k = 1 Output: "0" Explanation: S3 is "0111001". The first bit is "0". Example 2:

Input: n = 4, k = 11 Output: "1" Explanation: S4 is "011100110110001". The 11th bit is "1". Example 3:

Input: n = 1, k = 1 Output: "0" Example 4:

Input: n = 2, k = 3 Output: "1"

Constraints:

1 <= n <= 20 1 <= k <= 2n - 1

## Solutions

1. **recursion**

```cpp
class Solution {
public:
    char findKthBit(int n, int k) {
        if (n == 1) return '0';
        int num = (1 << n);
        // the middle character
        if (k == num / 2)
            return '1';
        else if (k < num / 2)
            return findKthBit(n - 1, k);
        else
            return findKthBit(n - 1, num / 2 - (k - num / 2)) == '1' ? '0' : '1';
    }
};
```